Partial correlation is a statistical technique that measures the correlation between two variables while controlling for the effects of one or more other variables.
For example, let’s say that we are interested in studying the relationship between a student’s test scores (variable A) and their GPA (variable B) while controlling for their class attendance (variable C). We can use partial correlation to determine whether there is a significant relationship between test scores and GPA, even when controlling for the effect of class attendance.
To calculate partial correlation, we first calculate the correlation coefficient between test scores and GPA (rAB). Next, we calculate the correlation coefficient between class attendance and both test scores (rAC) and class attendance and GPA (rBC). Finally, we use these values to calculate the partial correlation coefficient between test scores and GPA, controlling for class attendance (rAB.C).
The resulting value of rAB.C will indicate whether there is a significant relationship between test scores and GPA, even when controlling for the effect of class attendance. A value close to 1 would indicate a strong positive correlation between test scores and GPA, even when controlling for class attendance, while a value close to -1 would indicate a strong negative correlation.
In this example, if the rAB.C is still significant and positive, it means that the relationship between test scores and GPA is not explained by class attendance, and test scores and GPA have a positive correlation with each other, independently of class attendance.
